# How do you solve x + y = -1 and 6x – 2y = 18?

Mar 5, 2018

See a solution process below:

#### Explanation:

Step 1) Solve the first equation for $x$:

$x + y = - 1$

$x + y - \textcolor{red}{y} = - 1 - \textcolor{red}{y}$

$x + 0 = - 1 - y$

$x = - 1 - y$

Step 2) Substitute $\left(- 1 - y\right)$ for $x$ in the second equation and solve for $y$:

$6 x - 2 y = 18$ becomes:

$6 \left(- 1 - y\right) - 2 y = 18$

$\left(6 \times - 1\right) - \left(6 \times y\right) - 2 y = 18$

$- 6 - 6 y - 2 y = 18$

$- 6 + \left(- 6 - 2\right) y = 18$

$- 6 + \left(- 8\right) y = 18$

$- 6 - 8 y = 18$

$- 6 + \textcolor{red}{6} - 8 y = 18 + \textcolor{red}{6}$

$0 - 8 y = 24$

$- 8 y = 24$

$\frac{- 8 y}{\textcolor{red}{- 8}} = \frac{24}{\textcolor{red}{- 8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 8}}} y}{\cancel{\textcolor{red}{- 8}}} = - 3$

$y = - 3$

Step 3) Substitute $- 3$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 1 - y$ becomes:

$x = - 1 - \left(- 3\right)$

$x = - 1 + 3$

$x = 2$

The Solution Is:

$x = 2$ and $y = - 3$

or

$\left(2 , - 3\right)$

Mar 5, 2018

Solve algebraically or by graphing the equations.

$x = 2$
$y = - 3$

#### Explanation:

1. $x + y = - 1$
$6 x - 2 y = 18$
2. $6 x + 6 y = - 6$
$6 x - 2 y = 18$
Multiply each side of one or both equations by a constant so that one variable (in this case $x$) in both equations has the same coefficient (in this case $6$).
3. $6 x + 6 y = - 6$
$- \left(6 x - 2 y = 18\right)$
Subtract the second equation from the first using the distributive property $\left[a \left(b + c\right) = a b + a c\right]$.
4. $8 y = - 24$
$y = - 3$
Simplify and solve for $y$ by dividing both sides by $8$.
5. $x + \left(- 3\right) = - 1$
Plug $- 3$ in for y in one or both equations (the answer should be the same).
6. $x = 2$
Solve for $x$ (add $3$ to both sides).
7. $x = 2$
$y = - 3$
State the answer as $x$ and $y$ values or as a coordinate $\left(2 , - 3\right)$ when graphing the equations.